A Simplified Approach to Approximate Diffusion Processes Widely Used in Finance

Costabile, Massimo; Massabó, Ivar

doi:10.3905/jod.2010.17.3.065

Cited by 22 publications

(15 citation statements)

References 11 publications

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“…The algorithm is also flexible because it allows the use of other assumptions concerning the behavior of the underlying asset price, e.g., constant elasticity of variance specification, without much effort. Indeed, having chosen a procedure which makes recombining the discrete evolution of the underlying asset (cfr., Nelson and Ramaswamy [15], Costabile and Massabó [16], among others), the algorithm presented in this paper may be straightforwardly applied.…”

Section: Discussionmentioning

confidence: 91%

On pricing arithmetic average reset options with multiple reset dates in a lattice framework

Costabile

Massabó

Russo

2011

Journal of Computational and Applied Mathematics

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a b s t r a c tWe develop a straightforward algorithm to price arithmetic average reset options with multiple reset dates in a Cox et al. (CRR) (1979) [10] framework. The use of a lattice approach is due to its adaptability and flexibility in managing arithmetic average reset options, as already evidenced by Kim et al. (2003) [9]. Their model is based on the Hull and White (1993) [5] bucketing algorithm and uses an exogenous exponential function to manage the averaging feature, but their choice of fictitious values does not guarantee the algorithm's convergence (cfr., Forsyth et al. (2002) [11]). We propose to overcome this drawback by selecting a limited number of trajectories among the ones reaching each node of the lattice, where we compute effective averages. In this way, the computational cost of the pricing problem is reduced, and the convergence of the discrete time model to the corresponding continuous time one is guaranteed.

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Section: Discussionmentioning

confidence: 91%

On pricing arithmetic average reset options with multiple reset dates in a lattice framework

Costabile

Massabó

Russo

2011

Journal of Computational and Applied Mathematics

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“…Our lattice-based model overcomes this drawback by directly discretizing the original (heteroskedastic) spot rate process following the approach suggested in Costabile and Massabò (2010). This discretization scheme is based on a recombining binomial tree that converges weakly to the continuous diffusion process.…”

Section: Discussionmentioning

confidence: 99%

“…The first step of the algorithm is to provide a discretization for the spot rate process (2) using the approach recently suggested in Costabile and Massabò (2010). As usual, we start by dividing the claim lifetime T into n subintervals of equal length t = T /n.…”

Section: The Spot Rate Process Discretizationmentioning

confidence: 99%

“…We employ the procedure suggested in Costabile and Massabò (2010) to produce a simple lattice for Itô processes with regular coefficients, so making the discrete spot rate dynamics computationally feasible. The proposed approximating scheme guarantees the matching (at least within the limit) of the first two order moments of the original heteroskedastic process, which is usually unaffected by any singularity, thus avoiding the problem of matching the exploding drift of the transformed process.…”

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confidence: 99%

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A binomial approximation for two-state Markovian HJM models

2010

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“…To develop a tree based method in a dH context, we approximate the dynamics of both the squared volatilities in the asset price process by two recombining binomial lattices according to the approach proposed in [10]. Once the two univariate lattices have been established, we combine them into a "binomial pyramid" with each node branching into four.…”

Section: Introductionmentioning

confidence: 99%

On Pricing Contingent Claims Under the Double Heston Model

Costabile

Massabó

Russo

2012

Int. J. Theor. Appl. Finan.

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This article presents a lattice based approach for pricing contingent claims when the underlying asset evolves according to the double Heston (dH) stochastic volatility model introduced by Christoffersen et al. (2009). We discretize the continuous evolution of both squared volatilities by a "binomial pyramid", and consider the asset value as an auxiliary state variable for which a subset of possible realizations is attached to each node of the pyramid. The elements of the subset cover the range of asset prices at each time slice, and claim price is computed solving backward through the "binomial pyramid". Numerical experiments confirm the accuracy and efficiency of the proposed model.

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A Simplified Approach to Approximate Diffusion Processes Widely Used in Finance

Cited by 22 publications

References 11 publications

On pricing arithmetic average reset options with multiple reset dates in a lattice framework

On pricing arithmetic average reset options with multiple reset dates in a lattice framework

A binomial approximation for two-state Markovian HJM models

On Pricing Contingent Claims Under the Double Heston Model

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